To clarify, would you like the User-Provided Name to match exactly validFirstName & " " & validLastName or validLastName & ", " & validFirstName? If that’s the case, the conditional formatting rule could be written as shown below.

=OR(
    SUMPRODUCT(--(A1=(Checklist!$B$2:$B$9999&" "&Checklist!$A$2:$A$9999)))>0,
    SUMPRODUCT(--(A1=(Checklist!$A$2:$A$9999&", "&Checklist!$B$2:$B$9999)))>0
 )